Speeding up and slowing down the relaxation of a qubit by optimal control

TL;DR

This paper investigates how optimal quantum control can accelerate or decelerate the relaxation of a qubit towards its steady state, deriving analytical solutions and analyzing control constraints.

Contribution

It provides analytical expressions for optimal relaxation times under ideal and bounded control conditions, revealing limitations and possibilities of quantum control in relaxation processes.

Findings

Quantum control cannot speed up cooling if the initial state is hotter than the environment.

Strong control fields can enable the qubit to reach the fixed point in finite time if initially colder.

Unconstrained control allows indefinite maintenance of states far from the fixed point.

Abstract

We consider a two-level quantum system prepared in an arbitrary initial state and relaxing to a steady state due to the action of a Markovian dissipative channel. We study how optimal control can be used for speeding up or slowing down the relaxation towards the fixed point of the dynamics. We analytically derive the optimal relaxation times for different quantum channels in the ideal ansatz of unconstrained quantum control (a magnetic field of infinite strength). We also analyze the situation in which the control Hamiltonian is bounded by a finite threshold. As byproducts of our analysis we find that: (i) if the qubit is initially in a thermal state hotter than the environmental bath, quantum control cannot speed up its natural cooling rate; (ii) if the qubit is initially in a thermal state colder than the bath, it can reach the fixed point of the dynamics in finite time if a strong control field is applied; (iii) in the presence of unconstrained quantum control it is possible to keep the evolved state indefinitely and arbitrarily close to special initial states which are far away from the fixed points of the dynamics.